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In triangle A B C , if cotA cotC=1/2a n ...

In triangle `A B C ,` if `cotA cotC=1/2a n dcot B cotC=1/(18),` then the value of `tanC` is

Text Solution

Verified by Experts

Let `x=tan C`,
so `tan A=(2)/(x)` and `tan B =(18)/(x)`
As, in `triangle ABC,tan A+tan B+tan C=tan A tan B tan C`
`rArr (2)/(x)+(18)/(x)+x=(2)/(x).(18)/(x).x`rArr 20+x^(2)=36`
`rArr x=4tanC`
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